Suppose the Ajax Insurance Company provides insurance for skydivers whose wealth
ID: 1109828 • Letter: S
Question
Suppose the Ajax Insurance Company provides insurance for skydivers whose wealth before diving is $100,000. An accident will leave divers with a wealth of $80,000. The company divides the divers into two classes: safe (probability of an accident = 0.005) and unsafe (probability of an accident = 0.1). The utility of wealth for all divers is given by the function: U(w) = w0.5. If only the unsafe divers buy insurance, which compensates for half the losses, and the premium is $1,000, what profit will the insurance company expect to earn per insuree?
$0
$250
$500
$1,000
$0
$250
$500
$1,000
Explanation / Answer
ANSWER:
GIVEN-
wealth = $100000
loss in case of accident = $20,000
two types of divers - SAFE ; P(accident)= 0.005, P( no accident ) = 0.995
UNSAFE ; P( accident) = 0.1 , P( no accident) = 0.9
U(w) = 0.5 w
premium amount = $1000
only the unsafe diver buy insurance with half coverage i.e. coverage of $10000
TO FIND : profit of insurance company per insuree
SOLUTION:
Profit of the company = prob. of no accident * premium amount + prob. of accident * ( premium amount - coverage)
= 0.9 (1000) + 0.1( 1000- 10000)
= 900 - 0.1( -9000)
= 900 - 900
= 0
hence, the expected profit of the insurance company per insuree is $0.
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